Question: Michael is $12$ years older than Brandon. Seventeen years ago, Michael was $4$ times as old as Brandon. How old is Michael now?
Solution: We can use the given information to write down two equations that describe the ages of Michael and Brandon. Let Michael's current age be $m$ and Brandon's current age be $b$. The information in the first sentence can be expressed in the following equation: ${m = b + 12}$ Seventeen years ago, Michael was $m - 17$ years old, and Brandon was $b - 17$ years old. The information in the second sentence can be expressed in the following equation: ${m - 17 = 4(b - 17)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$, it might be easiest to solve our first equation for $b$ and substitute it into our second equation. Solving our first equation for $b$, we get: ${b = m - 12}$. Substituting this into our second equation, we get the equation: ${m - 17 = 4(} {(m - 12)}{ - 17)}$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 17 = 4m - 116$. Solving for $m$, we get: $3 m = 99$. $m = 33$.